A method of this kind is known from the German Patent Application DE 197 55 391 A1. It discusses first fabricating a ring from a sheet-metal strip and then of reshaping it into a supporting ring in a post-deformation process. The mutually contacting edges are joined together in a substance-to-substance bond by welding or soldering. The post-deformation can be accomplished by roll-forming or deep-drawing, it being possible for the supporting ring to be provided with different contours. Supporting rings must generally exhibit a superior surface quality, at least on the outer periphery thereof, since this surface forms a static sealing surface for sealing the sealing ring against a housing. This requires a good roundness profile and minimal roughness. When soldering is used for the joining process, it is disadvantageous that a good capillary effect is only attainable when the distance between the mutually contacting edges is small. It is also disadvantageous that the surfaces must be wettable. In the case of a substance-to-substance bond produced by welding, concave depressions frequently form at the join due to material creep. These concave depressions can result in leakiness of the sealing ring. Moreover, the edges of the sheet-metal strip must have a substantially uniform form.